Investigation of rice performance characteristics: A comparative study of LR, ANN, and RSM

Abstract Parboiling is a type of heat pretreatment used in rice processing to reach higher head rice yield and improve the nutrition properties of raw rice. In this research, the goals were prediction and determination of optimum conditions for parboiled rice processing using the response surface method (RSM) as well as modeling the output values by linear regression (LR) and artificial neural networks (ANN). The parameters including steaming time (0, 5, 10, and 15 min), dryer type (solar and continuous dryers), and drying air temperature (35, 40, and 45°C) were employed as input values. In addition, the breakage resistance (BR) and head rice yield (HRY) were selected as output values. The ANN‐based nonlinear regression, the multi‐layer perceptron (MLP), and the radial basis function (RBF) have been developed to model the process parameters, as well as the central composite design (CCD) was conducted for optimization of BR and HRY values. The outputs of RBF network have been successfully applied to predict higher coefficient of determination of BR and HRY as 0.989 and 0.986, respectively, indicating the appropriateness of the model equation in predicting head rice yield and breakage resistance when the three processing variables (steaming time, dryer type, and drying air temperature) are mathematically combined. Also, the lower root mean square error (RMSE) was obtained for each one as 0.043 and 0.041. The optimum values of BR and HRY were obtained as 12.80 N and 67.3%, respectively, at 9.62 min and 36.9°C for a solar dryer with a desirability of 0.941. In addition, the same values were obtained as 14.50 N and 72.1%, respectively, at 8.77 min and 37.0°C for a continuous dryer with a desirability of 0.971.

breakage resistance of kernels, broken rice ratio, grain hardness, and color are major determinants of milled rice acceptability by consumers (Campbell et al., 2009). During the processing and milling operation, rice kernels seem to be prone to crack which is uncontrollable to prevent in order to obtain the optimum head rice yield (HRY). Parboiling pretreatment causes a higher head rice yield with assumed minimal damage to grains by gelatinization of rice starch during processing time. This may be due to the role of gelatinization of starch in filling the voids and fissures (Hapsari et al., 2016). By measuring the three-point bending strength in some researches, it was found a significant relationship between the physical properties and HRY of rice and also a strong relationship between HRY and the percentage of kernels that could tolerate certain breakage force (Qi et al., 2003). There have been many studies on optimizing the processing conditions to limit waste and improve the HRY during the conversion of paddy (Aquerreta et al., 2007;Jindal & Siebenmorgen, 1987;Mukhopadhyay et al., 2019;Siebenmorgen et al., 2004;Steffe & Singh, 1980). Artificial neural networks (ANNs) are an attractive mathematical tool that potentially is configured for engineering purposes, such as pattern recognition, forecasting, and data compression. Multi-layer perceptron (MLP) network and radial basis function network (RBF) are the most common architectures of ANN (Raj & David, 2020). MLP network as a supplement of feedforward ANN is composed of input, hidden, and output layers. The RBF in its simplest form is a three-layer feed-forward neural network that uses radial basis functions as activation functions of the inputs and neuron parameters (Venkateswarlu & Jujjavarapu, 2019).
Presently, a well-trained ANN offers exciting possibilities to modeling and prediction in different fields of agriculture such as prediction of crop yield, seeding dates, and biomass production. The ANN is abundantly utilized to simulate various processes, particularly for some cases where other statistical modeling fails. Recently, there has been an increasing desire to apply ANN in agriculture due to faster prediction and possibility of adding or removing input and output variables compared to other conventional statistical models (Ghamari et al., 2010). Some researchers applied ANN models to estimate physical and physiological damage to seeds, determine the sugar content in fruits, estimate the crop yield, and moisture ratio of kernels during soaking. Results indicated that ANN models are the best methods for prediction because of its ability to modeling and classification in biological fields with more acceptable accuracy compared to other models (Kashaninejad et al., 2009;Khairunniza-Bejo et al., 2014;Khazaei et al., 2008;Liu et al., 2001;Oda et al., 2012;Saad & Ismail, 2009). In many works, researchers compared regression models and ANN to predict the crop yield and quality (Kim, 2008;Kumar, 2020;Stangierski et al., 2019). The response surface methodology (RSM) is a powerful mathematical modeling tool with a collection of empirical statistical techniques that is widely employed to find optimum conditions in varied processes to solve multivariable equations simultaneously by performing a minimal number of experimental runs (Betiku & Adesina, 2013;Danbaba et al., 2014;Karuppaiya et al., 2010;Mason et al., 2003). Danbaba et al. (2014) employed RSM involving central composite design (CCD) to study the effects of soaking temperature, steaming time, and drying time on the HRY of parboiled rice. They concluded that the research was conducted at the National Cereals Research Institute, Badeggi, Nigeria. Results indicated that regression coefficient of the developed model was significant (F-value 16.33 and p-value .003) indicating that most of the variation in head rice yield can be explained by the regression model. Coefficient of regression R 2 and adjusted R 2 were .97 and .91, respectively, indicating appropriateness of the RSM and CCD model in predicting optimum rice parboiling condition for maximum head rice recovery (Danbaba et al., 2014). In a similar study, RSM was successfully applied to optimize the processing conditions in grain production (Ghodke et al., 2009;Ogunbiyi et al., 2018). Despite numerous studies about the use of RSM and ANN strategy in several food research studies, scarce information has been reported on the application and comparison of mathematical models to predict HRY and BR of grains (in particular parboiled rice) under different processing conditions. The traditional method of studying one modeling method at a time can be effective in some cases, but it will be more useful to consider combined methods of possible model predicting and optimizing effective parameters for biological or physical processes. The RSM, LR, and ANN methods, which are based on statistical principles, can be applied as tools to implement process improvement strategy that will drive optimal HRY and BR from a given paddy lot by performing a minimal number of experiments. In addition, optimizing of process using RSM in combination with factorial experimental design of Box-Behnken design is essential for fitting a quadratic surface, which works well for process optimization. It has been investigated the impact of various parboiling processing conditions on rice characteristics by many researchers (Alkhafaji et al., 2020;Hunt, 2019;Likitrattanaporn & Noomhorm, 2011;Messia et al., 2012). Nevertheless, modeling and optimization of the processing of parboiled rice can improve the yield and its characteristics qualities. Meanwhile, different tools can be employed in modeling and optimization of experimental data for parboiling process. Such tools include RSM and ANN design, to mention but a few. In previous studies, researchers have reported the use of one or two software applications (Dash & Das, 2019;Dash & Das, 2021). However, the use of the combination of all three RSM, ANN, and LR methods, in modeling and optimization of parboiling process of paddy (in particular Hashemi paddy cultivar) has received little or no attention from the researchers. Its main advantage is the ability to compare statistically various results obtained from each of the above-mentioned software applications and eliminate the disadvantages of using a single one. In addition, the comparison among three methodologies shows certain differences in overall accuracy, sensitivity, and optimal result. Various parameters and evaluating "one-variable-at-a-time" could be time consuming, expensive, and inefficient. Thus, application of process modeling approaches including RSM and ANN is required and beneficial for optimization and modeling of paddy parboiling conditions. As rice kernels are very fragile during processing, determining the parboiling condition is very critical and needs great optimization and care. The main goal of the present study was to understand and compare the topography of the different methods (RSM, LR, and ANNs) in terms of fitting quality and optimization, to find a region where the most appropriate response occurs. A similar comparing study that was specifically developed to determine the maximum HRY and BR for Hashemi paddy cultivar parboiled in different conditions of steaming time (zero, 5, 10, and 15 min), dryer type (solar and continuous dryers), and inlet drying air temperature (35, 40, and 45°C) has not yet been reported.

| MATERIAL S AND ME THODS
The Iranian local rice cultivar of Hashemi, which is classified as a tall grain rice, was applied for parboiling experiments at Biosystems laboratory, University of Shiraz. After the harvesting process, the paddy was found to contain an initial moisture content of approximately 28 ± 1 (% w.b.). Before the different steps of experiments were done, sealed plastic bags were used to keep the rice samples that have been stored at 4 ± 1°C in a refrigerator. In this study, parboiling of paddy grains was accomplished by the conventional method that consists of soaking, steaming, and drying processes. Paddy samples were soaked in hot water at 80°C for 1 h. Open steaming step was then conducted following draining of water. Two drying modes of passive solar and continuous method were employed for drying.
Following the drying step, paddy grains were subjected to open aeration at room temperature for 1 week to reach a final moisture content of 11.5 ± 1°C. A testing rubber roll huller (Satake THU-35A, Japan) was then applied to dehusk the dried paddy samples. Many studies on the mechanical properties of grains reported that bending strength and fracture energy are a proper criterion to determine the performance of rice kernels (Lu & Siebenmorgen, 1995). On the other hand, due to difficulty of tensile strength tests for rice, the best option for testing is bending test (Nassiri & Etesami, 2015;. A three-point bending test was conducted by the Instron Testing Machine (STM-20 SANTAM, Iran) with a loading rate of 10 mm/s. In order to evaluate the sample breakage resistance in bending, two types of raw and parboiled dehusked samples (per type of 100 g of grain) were isolated by random selecting and then loaded by Instron jaw blades ( Figure 1).
Generally, the HRY was introduced as weight percentage of grains three-fourths or more of whole grain (in terms of head rice yield) or weight percentage of husked paddy (in terms of riceprocessing yield) to the total weight of milled rough rice (Farounk & Islam, 1995). In order to significantly improve the accuracy and acceleration of model performance, data value normalization was accomplished as follows (Lallahem & Mania, 2003): where X norm = normalized value, x = observed value, x min = minimum values, and x max = maximum values.
The measured data from these experiments were then used to optimize the design with all three RSM, ANN, and LR models with the objective of a maximal HRY and BR. Statistical comparison between the targets and predicted parameters was made using root mean square error (RMSE), mean absolute percentage error (MAPE), and the coefficient of determination (R 2 ).

| Linear regression (LR) model
Regression analysis is an effective statistical technique for examining parboiling pretreatment effects on mechanical properties of rice kernels. This approach is applied as a tool to estimate and model linear relationships (denoted by a best-fitted straight line) between variables and predict optimum response values using mathematical equations. Conventionally, the LR model is expressed as: (1) Measuring the breakage resistance of rice in three-point bending test using Instron machine where y = value of the dependent variable, x n = predictor variable, b n = coefficient value, e = observed error (uncontrolled factors and experimental error). The (b j ) is model parameters determined by a regression model.

| Artificial neural network (MLP, RBF) models
Neural networks can be applied as a direct substitute for autocorrelation, multivariable regression, LR, trigonometric, and other statistical analysis and techniques (Singh et al., 2003). Neural networks with respect to its unique aspects for pattern identify from complicated data can be used to present solutions in complex problems that may not be previously applied by common computer methods.
A trained neural network can be professionally exposed and modeled a set of categorized data to compare, simulate, optimize, and analyze response variables in terms of favorite situations. In addition, a multi-layer network technique detects best patterns using information sets for data mining and forecasting. In order to expose optimal outputs of network, the main premise is selection of Neuron Model (Single-Input Neuron, Transfer Functions, and Multiple-Input

Neuron) and Network Architectures (A Layer of neurons, Multiple
Layers of Neurons, and Recurrent Networks) (Simpson, 1991). Multilayer perceptron and radial basis function neural networks, as two of the neural architecture of ANN networks, can be used to simulate process outputs of regression problems with high accuracy (Kumar & Yadav, 2011;Lim et al., 2000). Radial basis function (RBF) compared with multi-layer perceptron (MLP) is responsive only to a limited part of input space, but MLP has more distributed approach.
In present study, the predictive performance of two different ANN architectures (MLP and RBF) was applied to the estimation of the BR and HRY. For the purpose of this study, the toolbox of ANN was applied to predict the nonlinear relationship between the input variables (steaming time, dryer type and drying air temperature) and the outputs (HRY and BR). The schematic of the ANN model used is presented in Figure 2. The data employed for experimental study were randomly divided into three groups: 70% in the training set, 15% in the validation set, and 15% in the test set. The structure of the three-layer feed-forward network studied in this paper was built using three input variables and two output variables to select the best predictive model.

| Multi-layer perceptron (MLP) model
The MLP neuron network is known as a common architecture for neural networks. The MLP consists of node (neuron) layers (an input layer, a hidden layer, and an output layer). The MLP model used activation function in all neurons to obtain an output by mapping of weighted sum of the inputs and bias terms. This arrangement presents a structure with feed-forward layered topology known as feedforward ANN (Alexandridis & Chondrodima, 2014). The MLP network is back propagated from an output layer to one or more hidden layers and, eventually, to an input layer, with a number of neurons in each layer. It was known the neuron connection between the input layers and hidden layers as the input weight matrix and neuron relationship between hidden layers and output layers is identified as the output weight matrix (Zhao et al., 2009). Each node or neuron, after calculating the sum of weighted input signals (x j , for j = 1, 2,…, n), creates a nonlinear activation function to generate output signal y as (Zarein et al., 2019): The function of Sigmoidal feedforward artificial neural networks that satisfies this criterion is expressed as (Dawson & Wilby, 1998): By comparison of neural network error measures, we can estimate the performance of the network. Error can be determined based on the difference between the targeted and predicted outputs. The error function can be evaluated as in the study cited herein (Zarein et al., 2019): where k = element index in the output vector, z pk = the k th element of the p th target pattern vector, p = the training pairs index of vectors, and z' pk = the k th element of the predicted vector when pattern p is expressed as input to the network.

| Radial basis function (RBF) neural network
In the field of linear and nonlinear data modeling, RBF model is based on supervised learning that commonly uses radial basis functions as activation functions. RBF networks is a popular alternative because of its mathematical simplicity, the computations relatively cheap, and also quick learning (learning in one stage) of the given application (Alexandridis & Chondrodima, 2014). This RBF neural network structure is similar to the MLP model except that it has a hidden layer with nodes as RBF units. Two main parameters of RBF model are location of the function's center and its deviation or width. The hidden unit determines the distance between an input data vector and the center of its RBF. The RBF gradually increased to a peak when the distance between the input vector x and its center vector declines to zero value. The output of the weights connecting the hidden layer to the output layer is a linear combination of RBFs of the inputs and neuron parameters that its processing is rapid (Foody, 2004). The output of RBF network is: where M = the number of basic functions, x = the input data vector, w kj = a weighted connection between the basis function and output layer, and Ø j = the nonlinear function of unit j, which is typically a Gaussian form.
where x = input of RBF unit, μ = the center of RBF unit, and σ j = the spread of the Gaussian basis function. Optimization of weights is done by least mean square (LMS) algorithm once the centers of RBF units are determined. In this study, centers were randomly selected from the data set.

| Response surface methodology (RSM)
The RSM is an efficient procedure widely used for designing, optimizing, developing, and analyzing new scientific and existing products. The RSM presents criteria to evaluate the effect of independent variables, alone or in combination, on processes. In addition, the RSM makes it possible to predict the most precise response using compilation of mathematical methods (Farooq Anjum et al., 1997;Halim et al., 2009). In order to determine the optimum value, Equation (8) is applied: where ß 0 = regression coefficients for intercept, ß i = linear coefficients, ß ij = interaction coefficients.
ß jj = quadratic coefficients, X i and X j = coded independent variables and ε = error.
In this study, central composite design (CCD) was carried out with 22 run and three center points. The performances of the LR, MLP, RBF, and RSM models were compared using statistical parameters of R 2 , MAPE, and RMSE as follows (Zarein et al., 2015): where z = the measured value, z' = the predicted value, N = the total number of observations (Armaghani et al., 2015;Garg et al., 2015).
R-squared (R 2 ) value is a statistical measure that is commonly between zero and one, and illustrates the ability of a parameter to predict another parameter. The maximum value for MAPE (100)  (6)  ues with a much higher coefficient of determination (R 2 = .98). It was found from ANOVA that the temperature, velocity, and bed depth had a significant effect on HRY at the 5% level (Rao et al., 2007).

| MLP model
In this study, several multi-layer perceptron networks with one or two layers and with 1-20 neurons were executed, trained, validated, and generalized to determine the best function. It was chosen an efficient approach based on MLP Back Propagation Neural Network to build the prediction models. MLP model runs by different steaming time, dryer type, and drying air temperature as input variables and the BR and HRY as output variables. In the case of the final chosen model of MLP, the most suitable structure with one input layer, three input variables, one hidden layer with 7 neurons, and one output layer with one output variable (3-7-1 structure) was selected. The predictive capability of the generated ANN models for HRY and BR was tested using unknown set of inputs data, and the predicted values and experimental values were plotted for HRY and BR as shown in Figure 4. With respect to observed cross-correlation among predicted and target values, it could be detected that MLP model was effective for the prediction HRY and BR of parboiled rice.

| RBF model
The

| Comparison of ANN models
The main objective of development of LR and ANN (MLP-RBF) models in this study was performance comparison of models to predict optimal BR and HRY. The observed results from linear regression analysis indicated that relationship between the output and input parameters is statistically unacceptable. The prediction models were developed with three inputs and two outputs and the networks were independently evaluated for each output. The ana-  ., 2004).

| Optimization and validation using RSM
A central composite design was successfully employed in this study to develop a relationship between rice performance characteristics (BR and HRY) and independent variables (steaming time, dryer type, and drying air temperature) in order to maximize the BR and HRY. The BR and HRY for both dryers was varied from 5.34 to 15.90 N and from 29% to 70%, respectively. The maximum BR (15.14 N) and HRY (70%)   (Joshi et al., 2008). Then the model was investigated by analysis of variance (ANOVA) that was conducted for fitting the model using Design-Expert software. ANOVA is an effective statistical method, which bifurcates into individual roots and allows user to find the sum of all the data variation in the model with specific sources of variation (Srikanth et al., 2018). Thus, the model variation is given in Table 3.  HRY values, the predicted conditions are as given in  Figure 8a) and the continuous dryer (Figure 8b). The best output was related to the HRY and BR for solar and continuous dryers, respectively.

TA B L E 3 Experimental process obtained for rice samples
A test was performed comparing the optimized BR and HRY values with their actual values to assess the validation for both dryers. The responses showed the low error rates (under 10%).  (Danbaba et al., 2014).
Prediction of HRY and BR under various processing conditions can be improved to commercial production quality and effective policymakers and other decisionmakers in the field of rice production. In this study, the high R 2 and low RMSE values for the HRY and BR variables showed that the ANN and RSM models can adequately predict and optimize the outputs, but more experimental data need to be gathered to obtain better accuracy of these parameters. In addition, it can be tested the accuracy of other modeling methods such as adaptive network-based fuzzy inference system and support vector regression to analyze rice parboiling process. 5. In general, results indicated that RSM, LR, and ANN could be successfully used to describe experimental data. All methods exhibited certain advantages, that is, ANN showed minor advantage of fitting quality, while RSM provided further insights into optimization of parboiling conditions.

ACK N OWLED G EM ENTS
The authors would like to thank Shiraz University for its facilities and technical support.